Answer
$-|m|=|-m|$ is sometimes true.
Work Step by Step
The negative (opposite) of an absolute value will always be negative, while an absolute value will never be negative. The only time this equation is true is when m is 0, since 0 and -0 have the same value.
For example, let m=-5.
$-|-5|\overset?=|-(-5)|$
$ -5\ne5$
For example, let m=0.
$-|0|\overset?=|-0|$
$ -0=0$
